Which expression correctly identifies the volume of a rectangular prism that has sides of 3.0 mm, 2.5 cm, and 12.4 cm?
A. V=(30 cm)(2.5 cm)(12.4 cm)
B. V=(3.0 mm)(25 mm)(124 mm)
C. V=(3.0 mm)(2.5 cm)(12.4 cm)
D. V=(3.0 mm)(25 mm)(12.4 cm)
While driving on the highway, Carl sees a sign that reads, "Buffalo 450 km." Carl checks his speedometer and notes that he is traveling at 70 miles per hour. How long will it take Carl to reach Buffalo at this speed? Round to one decimal place.
A. 4.0 hours
B. 10.3 hours
C. 2.5 hours
D. 6.4 hours
Mitch is tiling a bathroom shower that is 10 feet tall and comes in sections of 3 feet, 6 feet, and 3 feet long. He is using subway tiles that are 4 inches tall and 8 inches long. How many tiles will Mitch need to completely tile the shower if he does not rotate them? Round to the nearest whole number.
A. 2,066 tiles
B. 960 tiles
C. 4 tiles
D. 551 tiles
A box measures 9 inches by 9 inches by 12 inches. Estimate the volume of the box, and then find the actual volume. Use your estimation to determine if the answer is reasonable.
A. A good estimate is 900 cubic inches. The actual volume is 972 cubic inches. Since the actual volume is close to the estimate, the answer is reasonable.
B. A good estimate is 1,000 cubic inches. The actual volume is 972 cubic inches. Since the actual volume is close to the estimate, the answer is reasonable.
C. A good estimate is 900 cubic inches. The actual volume is 216 cubic inches. Since the actual volume is not close to the estimate, the answer is not reasonable.
D. A good estimate is 1,000 cubic inches. The actual volume is 216 cubic inches. Since the actual volume is not close to the estimate, the answer is not reasonable.
To find the volume of a rectangular prism, you need to multiply the lengths of its sides. Let's apply this approach to the given options.
Option A: V = (30 cm)(2.5 cm)(12.4 cm)
Option B: V = (3.0 mm)(25 mm)(124 mm)
Option C: V = (3.0 mm)(2.5 cm)(12.4 cm)
Option D: V = (3.0 mm)(25 mm)(12.4 cm)
To find the volume, we need to make sure that the units for all the sides are consistent. In this case, we should convert all the units to the same unit, such as millimeters or centimeters.
Option A has the correct units: (30 cm)(2.5 cm)(12.4 cm). So, Option A is the correct expression to calculate the volume.
Therefore, the correct answer is A. V = (30 cm)(2.5 cm)(12.4 cm).
To find the time it takes for Carl to reach Buffalo, we can use the formula:
Time = Distance / Speed
Given:
Distance = 450 km
Speed = 70 miles per hour
To use the formula, we need to convert either the distance or the speed to a consistent unit.
Let's convert the speed from miles per hour to kilometers per hour:
70 miles/hour = 70 * 1.61 km/hour = 112.7 km/hour
Now, we can plug the values into the formula:
Time = Distance / Speed
Time = 450 km / 112.7 km/hour ≈ 3.992 hours ≈ 4.0 hours (rounded to one decimal place)
Therefore, the correct answer is A. 4.0 hours.
To find the number of tiles needed to tile the shower, we need to calculate the area of the shower and the area of each tile.
Given:
Shower height = 10 feet
Shower sections = 3 feet, 6 feet, and 3 feet long
Tile height = 4 inches
Tile length = 8 inches
First, let's convert the measurements to the same unit:
Shower height = 10 feet = 120 inches
Shower sections = 3 feet + 6 feet + 3 feet = 12 feet = 144 inches
Now, calculate the area of the shower:
Shower area = height × length = 120 inches × 144 inches
Next, calculate the area of each tile:
Tile area = height × length = 4 inches × 8 inches
Now, divide the area of the shower by the area of each tile to find the number of tiles needed:
Number of tiles = Shower area / Tile area
Finally, round the result to the nearest whole number.
Calculating the exact number of tiles would involve multiplying large numbers, so let's focus on finding the approximate number of tiles needed.
The rough calculation would estimate the shower area as 120 × 144 square inches, and the tile area as 4 × 8 square inches.
Then, the approximate number of tiles needed would be (120 × 144) / (4 × 8). This would give us an estimate, so let's check the options to see which one is closest.
Calculating this rough estimate, we find that it is closest to option B: 960 tiles.
Therefore, the correct answer is B. 960 tiles.
To estimate the volume of a rectangular box, you need to multiply the lengths of its sides. The given box measures 9 inches by 9 inches by 12 inches.
Using estimation, rounding the lengths to the nearest whole number:
Length ≈ 9 inches
Width ≈ 9 inches
Height ≈ 12 inches
To estimate the volume, multiply the estimated lengths together:
Estimated volume ≈ 9 inches × 9 inches × 12 inches
This estimation gives us an answer close to 900 cubic inches.
Now, to find the actual volume, we multiply the exact lengths together:
Actual volume = 9 inches × 9 inches × 12 inches = 972 cubic inches
Comparing the estimate (900 cubic inches) to the actual volume (972 cubic inches), we can see that they are relatively close. Therefore, the answer is reasonable.
Therefore, the correct answer is A. A good estimate is 900 cubic inches. The actual volume is 972 cubic inches. Since the actual volume is close to the estimate, the answer is reasonable.
#1. recall that volume = length * width * height
#2. time = distance/speed -- watch the units (km vs miles)
#3. I assume he is tiling the walls, since no mention is made of the floor width.
8 in = 2/3 ft, so align the 8" sides with the lengths. Thus, the length is
(3+6+2) / (2/3) = 18 tiles long
and the room is 10ft/4in = 30 tiles high
So it will take 540 tiles
#4. 9x9x12 ≈ 10x10x12 = 1200
or, more roughly, 10x10x10 = 1000